"The purpose of this paper is to develop the fundamental concepts, especially those of measure, that are necessary to define the Lebesgue Integral. A rigorous definition of definite integral for a continuous function was first formulated by Cauchy at the beginning of the 19th century. This was then generalized to discontinuous functions by Riemann in the middle of the 19th century. But difficulties were encountered in the Riemann theory such as limits of Riemann-integrable functions (or even of continuous functions) may fail to be Riemann integrable. It was Lebesgue who first generalized the old process of integration of Cauchy-Riemann using the theory of measure, which has now almost eliminated the difficulty mentioned above, since limits of measurable functions are measurable"--Introduction. / Typescript. / "June, 1959." / "Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: H. C. Griffith, Professor Directing Paper. / Includes bibliographical references (leaf 30).
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_257285 |
| Contributors | Williford, William O. (authoraut), Griffith, H. C. (professor directing thesis.), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (iii, 30 leaves), computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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